Measurement of the $Dto K^-pi^+$ strong phase difference in $psi(3770)to D^0overline{D}{}^0$

We study $D^0overline{D}{}^0$ pairs produced in $e^+e^-$ collisions at $sqrt{s}=3.773$ GeV using a data sample of 2.92 fb$^{-1}$ collected with the BESIII detector. We measure the asymmetry $mathcal{A}^{CP}_{Kpi}$ of the branching fractions of $D to K^-pi^+$ in $CP$-odd and $CP$-even eigenstates to be $(12.7pm1.3pm0.7)times10^{-2}$. $mathcal{A}^{CP}_{Kpi}$ can be used to extract the strong phase difference $delta_{Kpi}$ between the doubly Cabibbo-suppressed process $overline{D}{}^{0}to K^-pi^+$ and the Cabibbo-favored process $D^0to K^- pi^+$. Using world-average values of external parameters, we obtain $cosdelta_{Kpi} = 1.02pm0.11pm0.06pm0.01$. Here, the first and second uncertainties are statistical and systematic, respectively, while the third uncertainty arises from the external parameters. This is the most precise measurement of $delta_{Kpi}$ to date.